Method and system to compensate for temperature and pressure in piezo resistive devices

ABSTRACT

A method and system to calibrate temperature and pressure in piezo resistive devices for non-linear sensors having two variables, where a piezo resistive device such as a piezo resistive transducer (PRT) used for example in a pressure sensor system is calibrated to calculate actual/ambient temperature and pressure even though the PRT impedance is unbalanced relative to pressure.

BACKGROUND OF THE INVENTION

The present invention relates generally to pressure sensors and, moreparticularly, to non-linear sensors having two variables withcross-dependency.

Piezo resistive devices, such as piezo resistive transducers (PRT), arecommonly used in commercial systems such as stress or pressure sensorsystems. Such PRTs are typically implemented in integrated circuits andsemiconductor devices. In accordance with the piezo resistive effect,the resistivity of piezo resistive elements changes in response tostrain from the applied mechanical or physical stress to the piezoresistive element. In integrated circuits and semiconductor devices, thepiezo resistive elements of the PRT are arranged to be in contact with adiaphragm such that a force or pressure applied to the diaphragm and thePRT converts the mechanical stress on the piezo resistive elements intodifferential electrical outputs. This property is used to measureambient pressure.

The resistivity of piezo resistive elements within PRTs exhibittemperature dependency. This property is used to measure ambienttemperature. If the PRT is not balanced with respect to pressure, largeerrors result in the computation of temperature. To minimize thispressure dependency of temperature computation, conventional PRTs aredesigned to be balanced with respect to pressure. However, attempting tobalance a PRT with respect to pressure is difficult to achieve andplaces a heavy constraint on the design and manufacture of PRTs.

Thus, there is a need for a method and system of calibration of piezoresistive devices to compensate for temperature and pressurecross-dependency that addresses or at least alleviates the above issuesin conventional non-linear sensors having two variables withcross-dependency.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings incorporated herein and forming a part of thespecification illustrate several aspects of the present invention and,together with the description, explain the principles of the invention.While the invention will be described in connection with certainembodiments, there is no intent to limit the invention to the describedembodiments. On the contrary, the intent is to cover all alternatives,modifications and equivalents as included within the scope of theinvention as defined by the appended claims. In the drawings:

FIG. 1 is a simplified circuit diagram of a configuration fortemperature measurement of an ideal piezo resistive transducer (PRT);

FIG. 2 is a simplified circuit diagram of a PRT configuration forpressure measurement;

FIG. 3 is a simplified block diagram showing a pressure sensor system;

FIG. 4 is a top plan view of a circuit layout of a piezo resistivesensor in accordance with an embodiment of the invention;

FIG. 5 is a cross-sectional view of the piezo resistive sensor of FIG. 4taken along line A-A in accordance with an embodiment of the invention;

FIG. 6 is a simplified circuit diagram of a configuration fortemperature measurement of an unbalanced PRT in accordance with anembodiment of the invention;

FIG. 7A is a flow chart of calculations for temperature recalibration ofa PRT in accordance with an embodiment of the invention;

FIG. 7B is a simplified block diagram showing a pressure sensor systemin accordance with an embodiment of the invention;

FIG. 8 is a graph of the absolute temperature accuracy of temperature (°C.) for several PRTs without recalibration;

FIG. 9 is a graph of the absolute temperature accuracy of temperature (°C.) for several PRTs with recalibration in accordance with an embodimentof the invention;

FIG. 10A is a flow chart of calculations for temperature cross-fit of aPRT in accordance with an embodiment of the invention;

FIG. 10B is a simplified block diagram showing a pressure sensor systemin accordance with an embodiment of the invention; and

FIG. 11 is a graph of the absolute temperature accuracy of temperature(° C.) for several PRT with temperature cross-fit in accordance with anembodiment of the invention.

DETAILED DESCRIPTION

In one embodiment of the present invention, a method of calibrating apiezo resistive device having a piezo resistive element with afluctuating resistivity in the piezo resistive device and signalsrepresentative of the temperature and pressure readings of the piezoresistive device includes calculating a first temperature as a functionof the signal representative of temperature reading of the piezoresistive device, and calculating an actual pressure as a function ofthe first temperature and the signal representative of pressure readingof the piezo resistive device.

Another embodiment of the invention comprises calculating an actualtemperature as a function of the first temperature and the actualpressure. The calculating of the actual temperature may be performedwith a constant of the actual pressure calculated for calibrating thepiezo resistive device. The constant may be determined empirically bydetermining a value of the constant of the actual pressure. Thecalculating of the first temperature may be a function of the signalrepresentative of temperature reading and the signal representative ofpressure reading. The first temperature may be an actual temperature,and calculating the actual pressure may be as a function of the actualtemperature and signal representative of pressure reading of the piezoresistive device. The piezo resistive device may be arranged within apressure sensor. The piezo resistive device may comprise at least fourpiezo resistive elements forming the piezo resistive device and eachpiezo resistive element having a fluctuating resistivity.

The present invention also provides a system of calibrating a piezoresistive device comprising a piezo resistive element having afluctuating resistivity in the piezo resistive device; and a processorfor receiving signals representative of the temperature and pressurereadings of the piezo resistive device; and calculating a firsttemperature as a function of the signal representative of temperaturereading of the piezo resistive device; and calculating an actualpressure as a function of the first temperature and signalrepresentative of pressure reading of the piezo resistive device.

An embodiment of the invention comprises calculating an actualtemperature as a function of the first temperature and the actualpressure. Calculating the actual temperature may be performed with aconstant of the actual pressure calculated for calibrating the piezoresistive device. The value of the constant may be determinedempirically of actual pressure readings. The calculating of the firsttemperature may be a function of the signals representative oftemperature reading and the pressure reading. The first temperature maybe an actual temperature. The calculating of the actual pressure may beas a function of the actual temperature and signal representative ofpressure reading of the piezo resistive device. The piezo resistivedevice may be arranged within a pressure sensor. An analogue to digitalconverter (ADC) may convert the signals representative of temperatureand pressure from the piezo resistive device and coupled to theprocessor. The piezo resistive device may be a piezo resistivetransducer. The piezo resistive device may comprise at least four piezoresistive elements forming the piezo resistive device and each piezoresistive element having a fluctuating resistivity. The piezo resistivedevice may be a non-linear sensor. The piezo resistive device may haveat least two variables that have cross-dependency.

A method and system is described to calibrate for temperature andpressure using piezo resistive devices. More generally, a method andsystem is described for non-linear sensors having two variables. A piezoresistive device such as a piezo resistive transducer (PRT) used forexample in a pressure sensor system is calibrated to calculateactual/ambient temperature and pressure even though the PRT impedance isunbalanced relative to pressure.

Referring now to FIG. 1 and FIG. 2, basic pressure and temperaturemeasurement configurations of piezo resistive transducers (PRT) areshown for illustration. Simplified circuit diagrams are shown of a PRT10 with temperature input 12 in FIG. 1, and a PRT 20 with pressure input22 and temperature input 24. In ideal PRTs, R is shown in resistorconfiguration 14 and is proportional to temperature, andR_(c)=R_(co)(1+αT) 16 is an on-chip resistor. vT 18, as a function oftemperature (T_(ambient)), is used to find and compensate vPT, where vPTis proportional to pressure (P_(ambient)) and vPT is also a function oftemperature (T_(ambient)), where vPT=f(P_(ambient), T_(ambient)) 28 anda voltage applied, such as for example voltage V_(ex)=1.75V.

FIG. 3 is a simplified block diagram showing the basic characteristicsof a pressure sensor module 30 within a pressure sensor system. Thepressure sensor module comprises PRT inputs of vT=f(T_(ambient)) andvPT=f(P_(ambient), T_(ambient)) to gain and analogue to digital (ADC)circuitry 32. The gain and ADC circuitry 32 is well known in theindustry and may have different configurations. For example the ADCcircuitry may be a sigma-delta A/D converter commercially available froma number of companies. The output of the gain and ADC circuitry 32,vT_(adc) and vP_(adc) is sent through datapath 34 for calculatingT=f(vT_(adc)) and P=f(vP_(adc), vT_(adc)). For example, T_(output) couldbe realized as a third order equation and P_(output) could be realizedas a first order equation as shown below.T _(output) =cT ₀ +cT ₁ ·T _(adc) +cT ₂ ·T ² _(adc) +cT ₃ ·T ³ _(adc)

The pressure equation may take the following form:P _(output) =C ₀ +C ₁ ·P _(adc) +C ₂ ·T+C ₃ ·P _(adc) ·T

A processing means such as an arithmetic logic unit (ALU), digitalsignal processor (DSP), or like processor, arranged in the datapath isused to compute the functions. It is clear from this implementation thatfor PRTs in which vT is strictly a function of T_(ambient), the abovemethod works well.

FIG. 4 is a top plan view of circuit layout of a piezo resistive sensor40 that may be implemented in accordance with an embodiment of theinvention. The piezo resistive sensor 40 comprises four piezo resistorsR1 41, R2 42, R3 43, R4 44 with leads 46 and circuitry 48. In thislayout, the four piezo resistors are located at the edge of a diaphragm49. The diaphragm 49 is shown transparent to show the orientation andplacement of the four piezo resistors under the diaphragm. Two piezoresistors R1,R2 are arranged in a perpendicular orientation relative tothe edge of the diaphragm. The other two piezo resistors R3,R4 arearranged in a parallel orientation relative to the edge of thediaphragm. The piezo resistors are sensitive to silicon strain caused bythe flexing of the diaphragm.

FIG. 5 shows a cross-section 50 of the piezo resistive sensor shown inFIG. 4 taken along line A-A and includes the cross-section of piezoresistors R1, R2. As the applied force or pressure 54 is applied to thediaphragm 49, where the diaphragm forms a vacuum 56, the resistance inpiezo resistors R1,R2 increases due to the tensile stress in thatdirection. The piezo resistors R3, R4 with the parallel orientationrelative to the diaphragm 49 decrease in resistance due to thecompressive stress in that direction.

FIG. 6 is a simplified circuit diagram of a realistic PRT 60 withtemperature measurement 62 and pressure measurement 63 in accordancewith an embodiment of the invention. Typically, in PRTs the followingbehaviour is observed:ΔR ₁ ≈ΔR ₂; and ΔR ₃ ≈ΔR ₄However,|ΔR ₁ |<|ΔR ₄|; and |ΔR ₂ |<|ΔR ₃|

As a result, R_(tot) 64 increases as pressure increases. Since,vT=V _(ex) *R _(tot)/(R _(tot)/(R _(tot) +R _(c)),

Where R_(c)=R_(co)(1+αT) 66, V_(T)=f(T_(ambient)) 68, α is the linearcoefficient of temperature of R_(c), and a voltage applied, such as forexample voltage V_(ex)=1.75V. This response of R_(tot) and hence vT isinherent in all PRT designs since the compressive and tensile stressesand piezo resistor sensitivities will never be perfectly balanced. It ispossible to minimize the magnitude of this effect, however, otheraspects of PRT performance is sacrificed as a result, such as asignificant reduction in transducer sensitivity.

FIG. 7A is a flow chart 70 of calculations for temperature recalibrationof a PRT in accordance with an embodiment of the invention. Thecalibration process requires three computations instead of the typicaltwo computations as discussed and shown above. The three calibrationsinclude calculating an intermediate or first temperature 72, actualpressure 74, and actual temperature 76 as the following: T₀=f(vT_(adc));P_(output)=f(T₀, vP_(adc)); and T_(output)=T₀+kP_(output), respectively.The order of the calculations is provided in accordance with obtainingthe necessary parameters, T₀->P_(output)->T_(output). The constant k isa constant of actual pressure P_(output) and may be found empirically.An example value for k found empirically is −0.75, where k can bederived by averaging the k value taken from a large number of samples.

FIG. 7B is a simplified block diagram 71 showing a pressure sensorsystem in accordance with an embodiment of the invention incorporatingthe calculations for temperature recalibration of a PRT as shown in theflow chart FIG. 7A.

For comparison and illustration, FIG. 8 and FIG. 9 show the differencethe temperature recalibration has on several PRTs in accordance with anembodiment of the invention. FIG. 8 is a graph 80 of the absolutetemperature accuracy of temperature (° C.) without recalibration, withT₀. FIG. 9 is a graph 90 of the absolute temperature accuracy oftemperature (° C.) with recalibration, with T=T₀+kP in accordance withan embodiment of the invention. The graph of FIG. 8 shows the banding orgrouping at different pressures which is eliminated in FIG. 9. The datashown in the graphs of FIG. 8 and FIG. 9 is taken from a samplesimulation of 16 PRTs.

FIG. 10A is a flow chart 100 of calculations for temperature cross-fitof a PRT in accordance with an embodiment of the invention. In thiscalibration process, the pressure dependency is built into thetemperature equation. Accordingly, this method requires twocomputations. The two computations include calculating first temperaturewhich is the actual temperature in this embodiment 102 and actualpressure 104 as the following: T_(output)=f(vT_(adc), vP_(adc)); andP_(output)=f(T_(output), vP_(adc)), respectively. The order of thecalculations is provided in accordance with obtaining the necessaryparameters, T_(output)->P_(output). With this method, higher order termscan be achieved then previously in pressure equations. The temperatureequation may take the following form:T=cT ₀ +cT ₁ ·T _(adc) +cT ₂ ·T ² _(adc) +cT ₃ ·T ³ _(adc) +cT ₄ ·T_(adc) ·P _(adc) +cT ₅ ·P _(adc)

The pressure equation may take the following form:P=C ₀ +C ₁ ·P _(adc) +C ₂ ·T+C ₃ ·P _(adc) ·T

The composite pressure equation may take the following form:P _(composite) =C′ ₀ +C′ ₁ ·P _(adc) +C′ ₂ ·T _(adc) +C′ ₃ ·T ² _(adc)+C′ ₄ ·T ³ _(adc) +C′ ₅ ·T _(adc) ·P _(adc) +C′ ₆ ·T ² _(adc) ·P _(adc)+C′ ₆ ·T ³ _(adc) ·P _(adc) +C′ ₇ ·T _(adc) ·P ² _(adc) +C′8·T ² _(adc)·P ² _(adc)

FIG. 10B is a simplified block diagram 101 showing a pressure sensorsystem in accordance with an embodiment of the invention incorporatingthe calculations for temperature cross-fit of a PRT where pressuredependency is built into the temperature equation as shown in the flowchart FIG. 10A.

FIG. 11 is a graph 110 of the absolute temperature accuracy oftemperature (° C.) for a PRT with temperature cross-fit in accordancewith an embodiment of the invention. The graph shows the plot of T_(err)curves for T=f(vT_(adc)) and T=f(vT_(adc),vP_(adc)) across temperature.

With this method, it is possible to obtain temperature accurately in thesemiconductor or integrated circuit such as an application specificintegrated circuit (ASIC). Therefore, it is not necessary to fabricatethe PRT to be balanced with respect to pressure as done in conventionalPRTs. The graph 110 of FIG. 11 also shows that the temperaturecalculation achieved is better than achieved by conventional methodsdespite an unbalanced PRT with respect to pressure. Additionally, theoverall order of pressure is 2 even though the pressure equation callsfor only 1^(st) order. This method also results in a savings in datapathcalculation 34 over conventional methods, as there are more terms thatare realized and considered in the pressure equation.

The above methods described in accordance with embodiments of theinvention may be implemented in the sensor system shown and describedabove with respect to FIG. 3, FIG. 7B and FIG. 10B, and with sensorshown in FIG. 4 and FIG. 5. It will be appreciated that other sensorsystems may implement the methods described here in accordance with theaspects and embodiments of the invention.

Embodiments of the invention have been described herein, including thebest mode known to the inventors for carrying out the invention.Variations of those preferred embodiments may become apparent to thoseof ordinary skill in the art upon reading the foregoing description. Theinventors expect skilled artisans to employ such variations asappropriate, and the inventors intend for the invention to be practicedotherwise than as specifically described herein. Accordingly, thisinvention includes all modifications and equivalents of the subjectmatter recited in the claims appended hereto as permitted by theapplicable law. Moreover, any combination of the above-describedelements in all possible variations thereof is encompassed by theinvention unless otherwise indicated herein or otherwise clearlycontradicted by context.

What is claimed is:
 1. A system of calibrating a piezo resistive device,comprising: a piezo resistive element having a fluctuating resistivityin the piezo resistive device; and a processor, coupled to the piezoresistive element, for receiving signals representative of temperatureand pressure readings of the piezo resistive element, calculating afirst temperature as a function of the signal representative of thetemperature reading, calculating an actual pressure as a function of thefirst temperature and the signal representative of the pressure reading,and calculating an actual temperature as a function of the firsttemperature, and the actual pressure times a constant (k).
 2. The systemof claim 1, wherein a value of the constant of the actual pressure isdetermined empirically.
 3. The system of claim 1, wherein calculatingthe first temperature is a function of the signal representative of thetemperature reading and the signal representative of the pressurereading.
 4. The system of claim 3, wherein the first temperature is anactual temperature.
 5. The system of claim 4, wherein calculating theactual pressure is a function of the actual temperature and the signalrepresentative of the pressure reading of the piezo resistive device. 6.The system of claim 1, wherein the piezo resistive device is arrangedwithin a pressure sensor.
 7. The system of claim 1, further comprisingan analogue to digital converter (ADC), connected between the piezoresistive element and the processor, for converting the signalsrepresentative of temperature and pressure from analog signals todigital signals read by the processor.
 8. The system of claim 1, whereinthe piezo resistive device is a piezo resistive transducer comprising atleast four piezo resistive elements and each piezo resistive element hasa fluctuating resistivity.
 9. The system of claim 1, wherein the piezoresistive device is a non-linear sensor and has at least two variablesthat have cross-dependency.